I give Musial and Gibson the edge because they continued their greatness with the Cardinals for longer (22 and 17 seasons, respectively). Never realized Hornsby only spent 10 there. I can see someone putting Pujols ahead of him, I guess.
For this purpose - who was the greatest player in the team's history - I'm more interested in a rate approach (over an extended period), by which Pujols appears to lead, but yet by so little that I'd fault no one in picking any of the three.
If we switch out "greatest" for like "most legendary," or identifiable," I'd definitely put Musical on a tier of his own, don't know where I'd head from there though.